*I have any child. *I have any children. *I have any money. *There is any hospital in our town. *There are any hospitals in our town. *There is any money on the table.

Interrogatives:

*Do you have any child? (But there are some special uses.) Do you have any children? Do you have any money? Is there any hospital in your town? Are there any hospitals in your town? Is there any money on the table?

Negatives:

*I don't have any child. (But there are some special uses.) I don't have any children. I don't have any money. There isn't any hospital in our town. There aren't any hospitals in our town. There isn't any money on the table.

The interrogative with any can be made correct in the right context.

-- Can you bring the package in your truck? -- I don't have a truck. -- Can you bring it in your car? -- I don't have a car. -- Do you have any vehicle? (Emphasize any with your voice.)

But you cannot start a conversation with, for example,Do you have any truck/car/vehicle? It must beDo you have a truck/car/vehicle?

The negative with any can be made correct in the right context.

-- Please enroll your son Eric in school by September 1. -- I don't have a son Eric. -- Excuse me. I mean your son Peter. -- I don't have a son Peter. I don't have any son.

-- Look at that beautiful bird! -- Where? -- There. In that tree. -- I don't see any bird.

This means that, provided you think up the right context, any of your examples might be correct. It's just that a few of them don't seem correct at all in isolation.

1. No significant difference. The use of a is just slightly more neutral sounding. 2. No significant difference. Possible use of a in the sense of (not) a single, thus expressing some surprise. 3. The "unmarked" version has the plural, but any doesn't require the plural (in my variety of English - see note below), as we see in these examples, which show a "marked" version. The plural is not OK in the given context, because only one vehicle is under consideration. any vehicle can be paraphrased here as even a single vehicle. 4. Same as for 3. The emphasis is on the singularity in question.

I am responding on the basis of how these sound to me in American English, by the way.